Europeans have been stunned and dismayed by the shutdown and near-default of the United States. Perhaps they even felt some schadenfreude. After all, European leaders have been held to ridicule and contempt for their global brinkmanship over the dysfunctional eurozone in recent years – time and again taking their economies to the cliff, only to pull back just before the markets opened.

Yet Europe might be in for its own version of a shutdown – less dramatic than the US government one, to be sure, but with similar causes. Just as the Tea Party has turned Congress into a paralysed, self-hating institution, an alliance of anti-European Union parties could give Europe its own version of "gridlock" if they win enough of the popular vote in next year's European elections. European elites – and any citizen who cares about the fate of the EU – better start thinking about that scenario.

The US and the EU share one characteristic: they are, in the jargon of political science, "mixed regimes", with a strong separation of powers and numerous checks and balances. This is good news for those who want laws to be based on broad consensus and generally to avoid what James Madison called "public instability". Unlike the Westminster model mixed regimes make it easy for a relatively small number of political players to veto change. They are also less transparent; plus it is harder to hold anyone clearly accountable – blame for politicking can always be shifted around.

Americans have been lamenting "gridlock" for years, but the founding fathers probably wanted things that way – to some extent. What the men at Philadelphia also hoped for was for politicians to become socialised into this system and learn how to work together. Except that the ideal of the gentleman-legislator who cuts backroom deals in the public interest seems plainly an illusion in the age of 24-hour news cycles and constant pressure from interest groups with seemingly unlimited financial and, ultimately, electoral fire-power.

The European parliament – though never exactly a beloved institution – was until recently more likely to live up to the US ideal, for the simple reason that most of its members had at least two things in common: they were broadly pro-EU and they were eager to guard the hard-won powers of the parliament and, wherever possible, expand them.

The parliament has actually become more influential than most Europeans realise, and not just on high-profile issues such as data protection. As the LSE professor Simon Hix has pointed out, approximately 25% of amendments to legislation proposed by the European parliament end up as law – more than in any national parliament.

Blueprints for making the EU more democratic have often focused on giving even more powers to MEPs – on the naïve assumption that the parliament would always automatically be pro-European. But what if it is captured by a European version of the Tea Party, a group that campaigns in the name of the principle that government itself is the problem? The Italian prime minister, Enrico Letta, warned in an interview with the New York Times this week that mainstream, pro-Europe parties must win at least 70% of the seats to avoid a "nightmarish legislature".

Letta's warning sounds very much like the EU establishment confirming the very reasons why populists condemn it: voters are allowed more democracy, as long as it remains a democracy without real choices – or so populists would charge. Hence it is important to be clear where the dangers lie exactly. Not every party that criticises the euro is anti-EU (think of the Alternative for Germany party). However, a significant number of truly anti-EU parties are simply destructive and suffer from fundamental contradictions. They claim democratic legitimacy on the basis of votes they received in elections to the European parliament and at the same time deny that the latter is democratic. They just want to shut the whole thing down (but ideally keep the money and the prestige that comes with the job).

As an illuminating study by Marley Morris has shown, anti-Europeans do little real work in the legislature, preferring to grandstand in plenary sessions – Ukip is a champion of this approach. Many of these parties – concentrated in the Europe of Freedom and Democracy (EFD) group, a kind of International of nationalists – offer no coherent policy platform.

Marine Le Pen's Front National (leading in French polls for the May 2014 European elections) and Geert Wilders' anti-immigration and anti-Islam party in The Netherlands are attempting to forge a pan-European anti-EU alliance. They might campaign more effectively together, but are also likely to make things even more chaotic: some populist parties will want nothing to do with the racism associated with them. On one level this incoherence is a good thing, as is the fact that even within the far right, alliances have regularly broken down.

So unless they truly want a dysfunctional EU, European citizens should think twice before they vote for such parties. They will not get different policies, but paralysis. There are real alternatives – even to austerity – and there is a genuine left-right spectrum of options in the parliament, more so than in many national parliaments. It is democratically legitimate to want to protest – but it is also important to take oneself and one's vote seriously. Shutdown is for political teenagers, not for adults.